1 Loading Libraries

library(psych) # for the describe() command
library(ggplot2) # to visualize our results
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
library(expss) # for the cross_cases() command
## Loading required package: maditr
## 
## To aggregate several columns with one summary: take(mtcars, mpg, hp, fun = mean, by = am)
## 
## Attaching package: 'expss'
## The following object is masked from 'package:ggplot2':
## 
##     vars
library(car) # for the leveneTest() command
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:expss':
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##     recode
## The following object is masked from 'package:psych':
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##     logit
library(afex) # to run the ANOVA and plot results
## Loading required package: lme4
## Loading required package: Matrix
## 
## Attaching package: 'lme4'
## The following object is masked from 'package:expss':
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##     dummy
## ************
## Welcome to afex. For support visit: http://afex.singmann.science/
## - Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
## - Methods for calculating p-values with mixed(): 'S', 'KR', 'LRT', and 'PB'
## - 'afex_aov' and 'mixed' objects can be passed to emmeans() for follow-up tests
## - Get and set global package options with: afex_options()
## - Set sum-to-zero contrasts globally: set_sum_contrasts()
## - For example analyses see: browseVignettes("afex")
## ************
## 
## Attaching package: 'afex'
## The following object is masked from 'package:lme4':
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##     lmer
library(emmeans) # for posthoc tests
library(ggbeeswarm) # for afex_plot

2 Importing Data

# import the dataset you cleaned previously
# this will be the dataset you'll use throughout the rest of the semester
# use ARC data
d <- read.csv(file="EAMMi2clean.csv", header=T)

# new code! this adds a column with a number for each row. it makes it easier when we drop outliers later
d$row_id <- 1:nrow(d)

3 State Your Hypothesis

One-Way: I predict that there will be a significant effect of political affiliation on mindfulness, defined by the degrees of non-judgmental-present-moment awareness participants report on the EAMMi2 15-item mindfulness questionnaire.

4 Check Your Variables

# you only need to check the variables you're using in the current analysis
# although you checked them previously, it's always a good idea to look them over again and be sure that everything is correct
str(d)
## 'data.frame':    3182 obs. of  8 variables:
##  $ ResponseId: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ politics  : int  2 1 2 8 1 8 4 2 8 4 ...
##  $ sex       : int  2 1 1 2 1 2 2 2 2 2 ...
##  $ moa       : num  3.2 3.1 3.05 2.3 3.1 3.35 3.65 3.7 3.55 2.95 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ stress    : num  3.3 3.6 3.3 3.2 3.5 2.9 3.2 3 2.9 3.2 ...
##  $ mindful   : num  2.4 1.8 2.2 2.2 3.2 ...
##  $ row_id    : int  1 2 3 4 5 6 7 8 9 10 ...
# Add new levels to the factor variable d$pol
levels(d$politics) <- c("1", "2", "3", "4", "5", "6", "7", "8")

# Recode the values in d$pol based on politics categories
d$pol[d$politics %in% c("1", "2", "3")] <- "liberal"
d$pol[d$politics %in% c("4", "8")] <- "moderate/apolitical"  # Combine "moderate" and "apolitical" into one level
d$pol[d$politics %in% c("5", "6", "7")] <- "conservative"

# Convert d$pol back to a factor
d$pol <- as.factor(d$pol)

# Check the updated table
table(d$pol)
## 
##        conservative             liberal moderate/apolitical 
##                 697                1380                1100
# make our categorical variables factors
#we'll actually use our ID variable for this analysis, so make sure it's coded as a factor
d$politics <- as.factor(d$politics)
d$row_id <- as.factor(d$row_id)

# we're going to recode our race/ethnicity variable into two groups: liberal and conservative
# table(d$politics)
#d$pol[d$politics == "1"] <- "liberal"
#d$pol[d$politics == "2"] <- "liberal"
#d$pol[d$politics == "3"] <- "liberal"
#d$pol[d$politics == "4"] <- "moderate"
#d$pol[d$politics == "5"] <- "conservative"
#d$pol[d$politics == "6"] <- "conservative"
#d$pol[d$politics == "7"] <- "conservative"
#d$pol[d$politics == "8"] <- NA
#table(d$pol)

#d$pol <- as.factor(d$pol)

# you can use the describe() command on an entire dataframe (d) or just on a single variable
describe(d$mindful)
##    vars    n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 3173 3.71 0.84   3.73    3.71 0.79 1.13   6  4.87 -0.06    -0.13 0.01
# we'll use the describeBy() command to view skew and kurtosis across our IVs
describeBy(d$mindful, group = d$pol)
## 
##  Descriptive statistics by group 
## group: conservative
##    vars   n mean   sd median trimmed  mad  min max range skew kurtosis   se
## X1    1 695 3.75 0.82   3.73    3.75 0.79 1.47   6  4.53 0.05    -0.18 0.03
## ------------------------------------------------------------ 
## group: liberal
##    vars    n mean   sd median trimmed  mad  min max range  skew kurtosis   se
## X1    1 1377 3.65 0.84   3.67    3.65 0.79 1.13   6  4.87 -0.03    -0.09 0.02
## ------------------------------------------------------------ 
## group: moderate/apolitical
##    vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 1097 3.76 0.85    3.8    3.78 0.89 1.2   6   4.8 -0.15    -0.16 0.03
# also use histograms to examine your continuous variable
hist(d$mindful)

# and cross_cases() to examine your categorical variables
cross_cases(d, politics, pol)
 pol 
 conservative   liberal   moderate/apolitical 
 politics 
   1  235
   2  772
   3  373
   4  568
   5  308
   6  332
   7  57
   8  532
   #Total cases  697 1380 1100

5 Check Your Assumptions

5.1 ANOVA Assumptions

DV should be normally distributed across levels of the IV All levels of the IVs should have equal number of cases and there should be no empty cells. Cells with low numbers decrease the power of the test (increase change of Type II error) Homogeneity of variance should be assured Outliers should be identified and removed Sampling distribution should be normal (if assumptions above are confirmed)

5.1.1 Check levels of IVs

table(d$pol)
## 
##        conservative             liberal moderate/apolitical 
##                 697                1380                1100
cross_cases(d, politics, pol)
 pol 
 conservative   liberal   moderate/apolitical 
 politics 
   1  235
   2  772
   3  373
   4  568
   5  308
   6  332
   7  57
   8  532
   #Total cases  697 1380 1100 
# our number of small nb participants is going to hurt us for the two-way anova, but it should be okay for the one-way anova
# so we'll create a new dataframe for the two-way analysis and call it d2

# d2 <- subset(d, pol != "apolitical")
# d2$pol <- droplevels(d2$pol)

# to double-check any changes we made
# cross_cases(d2, politics, pol)

5.1.2 Check homogeneity of variance

# use the leveneTest() command from the car package to test homogeneity of variance (we do not want significance)
# uses the 'formula' setup: formula is y~x1*x2, where y is our DV and x1 is our first IV and x2 is our second IV
leveneTest(mindful~pol, data = d)
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)
## group    2  0.6545 0.5198
##       3166
# worked!

5.1.3 Check for outliers using Cook’s distance and Residuals vs Leverage plot

5.1.3.1 Run a Regression

# use this commented out section only if you need to remove outliers
# to drop a single outlier, remove the # at the beginning of the line and use this code:
# d <- subset(d, row_id!=c(2972))

# to drop multiple outliers, remove the # at the beginning of the line and use this code:
# d <- subset(d, row_id!=c(561) & row_id!=c(855) & row_id!=c(2208))

# use the lm() command to run the regression
# formula is y~x1*x2 + c, where y is our DV, x1 is our first IV, x2 is our second IV, and c is our covariate
reg_model <- lm(mindful ~ pol, data = d) #for one-way
# reg_model2 <- lm(pss ~ gender_rc*poc, data = d2) #for two-way

5.1.3.2 Check for outliers (One-Way)

# Cook's distance
plot(reg_model, 4)

# Residuals vs Leverage
plot(reg_model, 5)

5.2 Issues with My Data

My cell sizes are unbalanced. A small sample size of total conservative participants serves as a less accurate representation, limiting the variable’s power and increasing the Type II error rate. Of the 3166 participants, most identify as liberal (1380), thus being the dominant population over the conservatives (697). The remaining 1100 participants are from the moderate and apolitical levels.I combined these into one level for robustness fo ananlysis. Though they do not pertain to the research question, it is essential to include more than two levels when conducting an ANOVA. Outliers in the moderate/apolitical level were not powerful enough to remove.

The results of Levene’s Test indicated that there was no significant difference in variances among the groups (F(2, 3166) = 0.6545, p = 0.5198).

6 Run an ANOVA

aov_model <- aov_ez(data = d,
                    id = "row_id",
                    between = c("pol"),
                    dv = "mindful",
                    anova_table = list(es = "pes"))
## Warning: Missing values for 13 ID(s), which were removed before analysis:
## 168, 216, 743, 1141, 1310, 1679, 1939, 2247, 2265, 2293, ... [showing first 10 only]
## Below the first few rows (in wide format) of the removed cases with missing data.
##        row_id                 pol  .
## # 168     168 moderate/apolitical NA
## # 216     216             liberal NA
## # 743     743                <NA> NA
## # 1141   1141             liberal NA
## # 1310   1310        conservative NA
## # 1679   1679        conservative NA
## Contrasts set to contr.sum for the following variables: pol
# aov_model2 <- aov_ez(data = d2,
                   # id = "X",
                    # between = c("gender_rc","poc"),
                   # dv = "pss",
                   # anova_table = list(es = "pes"))

7 View Output

Effect size cutoffs from Cohen (1988):

  • η2 = 0.01 indicates a small effect
  • η2 = 0.06 indicates a medium effect
  • η2 = 0.14 indicates a large effect

8 Regarding effect size – .01 to .05 is small, so .005 would be considered trivial or not meaningfully significant.

nice(aov_model)
## Anova Table (Type 3 tests)
## 
## Response: mindful
##   Effect      df  MSE        F  pes p.value
## 1    pol 2, 3166 0.71 6.96 *** .004   <.001
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

9 Visualize Results

afex_plot(aov_model, x = "pol")

10 Run Posthoc Tests (One-Way)

A significant effect of political affiliation on mindfulness was observed (F(1, 3166) = 6.96, p = .004), indicating that individuals’ political affiliation had a statistically significant impact on their level of mindfulness.

emmeans(aov_model, specs="pol", adjust="sidak")
##  pol                 emmean     SE   df lower.CL upper.CL
##  conservative          3.75 0.0319 3166     3.68     3.83
##  liberal               3.65 0.0227 3166     3.59     3.70
##  moderate/apolitical   3.76 0.0254 3166     3.70     3.82
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates
pairs(emmeans(aov_model, specs="pol", adjust="sidak"))
##  contrast                             estimate     SE   df t.ratio p.value
##  conservative - liberal                0.10840 0.0392 3166   2.768  0.0156
##  conservative - (moderate/apolitical) -0.00658 0.0408 3166  -0.161  0.9858
##  liberal - (moderate/apolitical)      -0.11498 0.0341 3166  -3.376  0.0021
## 
## P value adjustment: tukey method for comparing a family of 3 estimates

11 Write Up Results

11.1 One-Way ANOVA

The aim of this study was to examine the impact of political affiliation on reported mindfulness in participants of the EAMMi2 data set. To test my hypothesis that there would be a significant effect of political affiliation on mindfulness, I used a one-way ANOVA for three levels of my politics variable (conservative, liberal, moderate/apolitical). Results indicate that there is a significant difference in mindfulness (measured with a 15-item questionnaire) scores between individuals with conservative political affiliation (M = 3.75, SE = 0.0319) and those with liberal political affiliation (M = 3.65, SE = 0.0227). Moderate/apolitical was M = 3.76, SE = 0.0254. The contrast analysis revealed that the conservative group had higher levels of mindfulness compared to the liberal group (estimate = 0.10840, p = 0.0156), though this finding is not significant. therefore, the null hypothesis cannot be ruled out.

Limitations to this study include unbalanced data: my sample consisted of 3166 participants, with a larger proportion identifying as liberal (n = 1380, 43.6%) compared to conservatives (n = 697, 21.6%), while moderate/apolitical participants comprised the remaining population (n = 1100, 34.7%). This significantly reduces the power of our test and increases the chances of a Type II error because of the liberal sample size dominance. A non-significant Levene’s test (p = 0.5198) assumes homogeneity of variance in my data.

Findings show a significant effect of political affiliation on mindfulness, (F(1, 3166) = 6.96, p > .001), ηp2 = .004 (Cohen, 1988). Despite the trivial contribution of political affiliation on mindfulness, this factor should still be considered when making observations.

## [1] "conservative"        "liberal"             "moderate/apolitical"

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.